No-Elimination example (FWD)

[Donald E Davison]

  ----------- Forwarded Letter -----------
To: Donald E Davison <donald at mich.com>
From: Blake Cretney <bcretney at postmark.net>
Subject: No-Elimination example
Date: Wed, 17 Feb 1999 00:23:31 +0000

What would Run-off Without Elimination do with these ballots?

35 A B
25 B
40 C B

I get that B would win, which contradicts your statement that this
method will be equivalent to IRV in all 3 candidate cases.

---
Blake Cretney
See the EM Resource:  http://www.fortunecity.com/meltingpot/harrow/124
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Dear Blake Cretney,

     I stand corrected.

     You are showing a very good example of strategic voting.
     Faction B wisely told their supporters to only vote for one candidate.
     This is how a faction can gain an edge in an electon.
     When every faction does this, then the election is reduced down to
Plurality.
     This is the flaw of Run-Off without Elimination, but it is also the
flaw of Run-Off with Withdrawal, Approval Voting, and of Condorcet.
     All the Compromise Candidate(CC) methods have this flaw.
     Choice Run-Off(IRV) does not have this flaw.

Donald
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To: donald at mich.com (Donald E Davison)
From: Blake Cretney <bcretney at postmark.net>
Subject: Re: No-Elimination example
Date: Mon, 22 Feb 1999 06:32:54 +0000

It's important not to confuse two similar statements:
1.  Ranking only your favourite can sometimes cause your favourite to
be elected.
2.  Ranking only your favourite makes it more likely that your
favourite will be elected.

It's pretty clear that neither is true of IRV, run-off, or plurality.
 I think both are true for Run-off without Elimination.  Given time, I
could probably come up with a proof.  It's obvious that both are true
of Approval.

In the Condorcet methods I've seen, #1 is true, but #2 is false.
This means that it is not a sensible strategy in Condorcet for every
faction to tell its supporters to vote only for it.  As a result the
problem you mention won't occur for a Condorcet method, like Path
Voting.

Consider the following example, which I will resolve using Path
Voting, described at
http://www.fortunecity.com/meltingpot/harrow/124/path

40 A B C
35 B C A
25 C A B

A>B 65-35=30
B>C 75-25=50
C>A 60-40=20

(A B C)
C>A 20 contradicted by A>B>C, dropped
A>B 30 holds, B>C
A (B C)

A is the winner.

Now, consider if the A-1st faction had only voted for A.

40 A
35 B C A
25 C A B

A>B 65-35=30
B>C 35-25=10
C>A 60-40=20

(A B C)
B>C 10, C>A>B
C>A 20, A>B
C (A B)

C is the winner.  So, the vote-for-1st-only strategy not only cost
the A-1st voters the election, it elected their last choice.

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Blake